Errors of single-mirror or prism Hertel exophthalmometers and recommendations for minimizing the errors.

PURPOSE: Analysis is performed of the geometry of a Hertel exophthalmometer to determine the intrinsic error of reading that results from using the instrument in the manner that the manufacturer intended. Recommendations for improvement of the design and/or use of the instrument are made based on the findings. METHODS: A schematic drawing of the manufacturer-recommended use of an exophthalmometer is created. The geometry is analyzed to reveal the sources of error in the exophthalmometer reading and an equation for the magnitude of the error is derived. RESULTS: The exophthalmometer reading error is directly proportional to the difference between the reading obtained and the reading at the no-parallax-alignment position used to make the reading (commonly 18 mm), with the reading being low when the reading is greater than the no-parallax-alignment position and high when the reading is less. The error is increased by the observer's eye being closer to the reflecting surface and by widening the base or separation of the 2 reflecting surfaces of the instrument. The exophthalmometer reading may be 1.7 mm less than actual when it reads as 35 mm, which is 17 mm from the no-parallax-alignment position. CONCLUSIONS: To minimize error in exophthalmometer readings, the reading should be as close to the no-parallax-alignment-position as possible. Exophthalmometers should therefore be modified to have multiple sets of no-parallax-alignment lines, each pair of a different color. The instrument should be used with the narrowest feasible base and the examiner should be consistently positioned as far from the reflecting surface of the instrument as possible.